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A096558 Output of the linear congruential pseudo-random number generator rand() used in Microsoft's Visual C++.

%I A096558 #23 Aug 29 2024 09:14:41
%S A096558 0,38,7719,21238,2437,8855,11797,8365,32285,10450,30612,5853,28100,
%T A096558 1142,281,20537,15921,8945,26285,2997,14680,20976,31891,21655,25906,
%U A096558 18457,1323,28881,2240,9725,32278,2446,590,840,18587,16907,21237,23611,12617
%N A096558 Output of the linear congruential pseudo-random number generator rand() used in Microsoft's Visual C++.
%H A096558 Alois P. Heinz, <a href="/A096558/b096558.txt">Table of n, a(n) for n = 1..10000</a>
%H A096558 <a href="/index/Ps#PRN">Index entries for sequences related to pseudo-random numbers.</a>
%F A096558 b(1)=0, b(n)=(b(n-1) * 214013 + 2531011) mod 2^32. a(n) = (floor(b(n)/65536) mod 32768). The sequence is periodic with period length 2^32.
%F A096558 a(n) = floor(A096557(n)/2^16) mod 2^15 = floor((2531011*(214013^(n-1)-1)/214012 mod 2^32)/2^16) mod 2^15. - _M. F. Hasler_, May 14 2015
%p A096558 b:= proc(n) option remember; `if`(n<2, 0,
%p A096558       irem(214013 *b(n-1) +2531011, 4294967296))
%p A096558     end:
%p A096558 a:= n-> irem(iquo(b(n), 65536), 32768):
%p A096558 seq(a(n), n=1..50);  # _Alois P. Heinz_, Jun 10 2014
%t A096558 A096557 = NestList[Mod[#*214013 + 2531011, 2^32] &, 0, 50];
%t A096558 Mod[BitShiftRight[A096557, 16], 2^15] (* _Paolo Xausa_, Aug 29 2024 *)
%o A096558 (PARI) a(n)=A096557(n)>>16%2^15 \\ _M. F. Hasler_, May 14 2015
%o A096558 (PARI) A096558(n)=lift((Mod(214013, 2^34)^(n-1)-1)*13129821757)>>18%32768 \\ _M. F. Hasler_, May 14 2015
%Y A096558 Cf. A096557 corresponding internal states. A096550-A096561 other pseudo-random number generators.
%K A096558 nonn,easy
%O A096558 1,2
%A A096558 _Hugo Pfoertner_, Jul 21 2004